Problema Solution
John rode his motorbike for a distance of 30 km
from his house to the General Hospital. If he
incresed his average speed by 10 km / h, the time he
takes to complete his journey will be reduced by 30
minutes. Calculate his initial average speed.
Answer provided by our tutors
Let
d = 30 km the distance
v = initial average speed, v>=0
v + 10 = increased average speed
t = the time needed when traveling at rate v (in hours)
t - 30/60 =t - 0.5 the time needed when traveling at rate v + 10
Since d = v*t we ahve:
vt = 30
(v + 10)(t - 0.5) = 30
From vt = 30 we have t = 30/v.
Plug t = 30/v into (v + 10)(t - 0.5) = 30:
(v + 10)(30/v - 0.5) = 30
........
click here to see the equation solved for v
........
v = 20 km/h
The initial average speed was 20 km/h.